How do SOC and C-rate affect steady-state polarization voltage? Key insights for battery testing

Steady-state polarization voltage is governed primarily by both charging C-rate and initial SOC. At a fixed initial SOC, increasing the charging rate—for example, from C/3 to 1C—generally increases the magnitude of the steady-state polarization voltage. At a fixed C-rate, the relationship with initial SOC is nonlinear: polarization is highest near the low- and high-SOC limits and relatively low across the middle SOC range.

The practical implication is that polarization cannot be modeled with one fixed resistance or RC parameter. Testing equipment and battery models should account for both the applied C-rate and the cell’s initial SOC, with special attention to SOC below approximately 10% and above approximately 80%.

How C-Rate Changes Polarization Voltage

Higher charging current produces larger polarization

During constant-current charging, a higher C-rate drives a larger departure between the cell’s equilibrium voltage and its measured terminal voltage. This appears as a larger steady-state polarization voltage after the transient response has settled.

For example, increasing the charge rate from C/3 to 1C generally increases polarization magnitude. In many cells, the relationship is approximately proportional over a defined operating range, although the exact slope depends on chemistry, temperature, SOC, and aging.

The current effect reflects internal electrochemical limitations

Higher current increases ohmic voltage drop, charge-transfer overpotential, and concentration polarization. These effects may be represented in a battery model through current-dependent resistance and RC polarization coefficients.

At particular operating points, such as a low-SOC inflection region, the established polarization amplitude may be approximated with a linear relationship:

[ U_p = aI + b ]

This is useful for parameter fitting, but it should not be treated as a universal relationship across the full SOC range.

How Initial SOC Changes Steady-State Polarization

The SOC relationship is bowl-shaped

When charging conditions are held constant, steady-state polarization voltage is typically higher at very low and very high initial SOC. It remains lower and comparatively stable through the middle region, approximately 10%–70% SOC.

This produces a bowl-shaped trend when polarization voltage is plotted against initial SOC: high near the SOC boundaries and lower across the central operating range.

Low SOC creates an early polarization peak

Polarization can become especially pronounced below approximately 10% SOC, with a peak often observed near 5% SOC. The cell’s electrochemical response is therefore not well represented by a model calibrated only in the mid-SOC region.

A test that begins near full discharge may show a rapid rise toward a steady-state polarization level that is substantially different from the result of an otherwise identical test beginning at 30% or 50% SOC.

High SOC produces another increase

Polarization rises again as the cell approaches the upper SOC range, becoming significant above approximately 80% SOC and often increasing strongly between 80% and 90% SOC during constant-current charging.

Once charging transitions into the constant-voltage stage, current tapers and polarization can decline. Therefore, the high-SOC behavior must be interpreted in the context of the CC-to-CV transition, rather than treated as a simple continuation of constant-current behavior.

Why Initial SOC Must Be Included in Cell Models

One fixed parameter set is insufficient

Because the steady-state polarization level depends on initial SOC, a single fixed polarization resistance or time constant will generally produce inaccurate predictions across the full charge window.

A model calibrated in the 10%–70% SOC region may underpredict voltage polarization near the lower and upper SOC extremes. Conversely, parameters fitted at an extreme SOC may overstate polarization in the middle range.

The transient response also depends on initial SOC

Polarization voltage may rise sharply from its initial value before reaching a SOC-dependent steady state. The model must therefore capture both:

• The transient response, represented by dynamic elements such as RC networks.
• The final polarization level, adjusted for initial SOC and charging current.

Initial SOC distortion factors and SOC-dependent polarization coefficients are appropriate ways to represent this behavior in an equivalent-circuit or parameterized battery model.

Initial conditions must be controlled during testing

Initial SOC is meaningful only when the cell’s preparation history is also controlled. Rest time, prior charge or discharge direction, temperature, and SOH can alter the initial polarization state and therefore change the measured response.

For repeatable testing, define the initial SOC, rest duration, preceding operating direction, temperature, and charge rate before comparing polarization results.

What This Means for Battery Testing Equipment

Test across both SOC and C-rate

A useful characterization matrix varies at least:

• Initial SOC: including low, middle, and high SOC regions.
• Charging C-rate: for example, C/3, 1C, and higher rates where appropriate.
• Rest condition: sufficient and consistent relaxation before each test.
• Cell condition: including different SOH levels when lifecycle behavior matters.

This separates current-driven effects from SOC-driven effects and prevents the equipment from fitting one influence as if it were the other.

Capture the settled value, not only the initial voltage jump

The initial voltage response contains transient information, but steady-state polarization requires a defined settling criterion. The test system should record the time evolution and identify when the voltage has approached its stable value under the selected charging condition.

The appropriate settling time depends on the cell and the model bandwidth. Using the same criterion for every SOC and C-rate improves comparability.

Use smaller currents near SOC extremes

High polarization at very low and very high SOC reduces charging capability and can increase stress, heat generation, and degradation risk. Charging protocols should therefore consider reducing current near these regions rather than applying the same high C-rate across the entire SOC range.

This is particularly important when validating fast-charging strategies or operating cells close to their voltage limits.

Understanding the Trade-offs

Higher C-rates improve test efficiency but increase distortion

A higher C-rate shortens the time required to characterize a cell and reveals rate-dependent behavior. However, it also increases polarization, thermal effects, and the risk that the measured voltage reflects aggressive operating conditions rather than the cell’s nominal behavior.

High-rate data should therefore be labeled clearly and should not be used as a direct substitute for low-rate equilibrium characterization.

Extreme-SOC measurements are important but less forgiving

Testing below 10% or above 80% SOC is essential for validating limits and charging controls because polarization is elevated there. These regions are also more sensitive to current, relaxation history, temperature, and cell-to-cell variation.

Additional safeguards and tighter test conditions are justified when collecting data near the SOC boundaries.

A simple linear current model has limited scope

The approximate relationship (U_p=aI+b) can simplify parameterization at a selected SOC or inflection point. It does not eliminate the need for SOC-dependent modeling because polarization changes nonlinearly across the complete charge range.

Using a local linear fit as a global model can produce errors near the low- and high-SOC regions and during the CC-to-CV transition.

Aging changes the measured polarization

As SOH declines, charging polarization generally increases. A model that ignores aging may interpret this increase as a C-rate or SOC effect and consequently misestimate the cell’s internal resistance or dynamic parameters.

For lifecycle studies, include SOH-dependent correction factors or periodically recalibrate the polarization parameters.

Making the Right Choice for Your Goal

Use the testing strategy that matches the behavior you need to predict.

• If your primary focus is mid-SOC operation: Characterize across approximately 10%–70% SOC and use multiple C-rates to identify the current dependence of the relatively stable polarization region.
• If your primary focus is fast charging: Include dense measurements below 10% and above 80% SOC, where high C-rates produce disproportionately important polarization behavior.
• If your primary focus is model accuracy: Use SOC- and current-dependent polarization parameters rather than one fixed resistance or RC parameter set.
• If your primary focus is repeatable laboratory comparison: Standardize initial SOC, rest time, prior charge/discharge history, temperature, and SOH.
• If your primary focus is safe charging control: Reduce current near low- and high-SOC extremes and account for the CC-to-CV transition when interpreting polarization data.

Accurate steady-state polarization modeling requires treating C-rate as a magnitude driver and initial SOC as a nonlinear operating-state factor.

Summary Table:

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